A particularly robust framework for tackling such a problem was provided by the geometric quantum theory approach, developed over the years by many authors (e.g., [1]}[2]}) with the basic premise of reformulating the complex Hilbert space as a genuine manifold of states with additional structure — i.e. symplectic, Riemannian (i.e. metric), and complex. The modifications proposed within this framework typically boiled down to two chief maneuvers: either (a) keeping the symplectic structure intact, but changing the dynamics, mainly by changing the Hamiltonians, or (b) modifying the geometric structures themselves. The latter is certainly a more difficult endeavor; and has been discussed, for example, by Cirelli et al. [3]}[4]} as well as by Schilling [2]} and company [6]}. The former is simpler to implement, and many of the proposed extensions, for example by Weinberg [7]} or Kibble [1]}[9]}, are exactly of this type.
